Multiscale characteristics of electrical contact resistance

The flow of electrical current through a microscopic actual contact spot between two conductors is influenced by the flow through adjacent contact spots. A smoothed version of this interaction effect is developed and used to predict the contact resistance when the statistical size and spatial distribution of contact spots is known. To illustrate the use of the method, the Archard multiscale contact model is adopted to calculate the distribution of the contact spot and an electrical contact resistance. We compare the results of statistical approach with the results of deterministic approach. In the statistical approach, the statistical density function for the mean size of contact spots is estimated by kernel estimation. With these assumptions, it is shown that including finer scale detail in the fractal surface causes the predicted resistance to approach a finite limit. To model the clustering effects of micro contacts, it is essential to include higher order moments in the statistical distribution. To show the practical implementation of the method to the real surface, idealized fractal rough surface is defined using the random midpoint displacement algorithm and the size distribution of contact spots is assumed to be given by the intersection of this surface with a constant height plane.